You're completely right.

Basically, you know the Capacitance, and you're giving the function of current with respect to time. Since you can just Integrate your I function with respect to t.

Just use a simple u substitution so that

and

From there, you can just integrate the function as

and you will end up with the answer

Change your back into

Once you plug in your limits of 0 and 2 you will get

You know that so your final result should be